nt axis A disk of mass m and radius R, which is wound with a rope hanging from the ceiling, starts to roll down. The linear velocity of the ball when it has rolled 5 m down can be expressed as v = V (square root of a/b) where a and b are the smallest possible integers. Find the value of a+b. O Cannot calculate without values of m and R O 201 O 200 O 203

In a laboratory test of tolerance for high acceleration, a pilot is swung in a circle 15.0 m in diameter. It is found that the pilot blacks out when he is spun at 30.6 rpm (rev/min). At what acceleration (in SI units) does the pilot black out? acceleration: 77.01 m/s? Express this acceleration in terms of a multiple of g. acceleration as a multiple of g: 7.858 If you want to decrease the acceleration by 22.0% without changing the diameter of the circle, by what percent must you change the time for the pilot to make one circle? percent of time change:

E. The centripetal acceleration of a particle moving in a circle is given by the formula a = s²/r where r is the radius and s is the speed of the particle. a) Consider a as a function of s and r. Compute the differential of a. b) Suppose that the particle is moving with speed 50cm/sec and the radius is 10cm. Use the differential to estimate the change in centripetal acceleration if the radius is changed to 9.80cm and the speed is changed to 51cm/sec. (Answ: 15) c) Suppose that the speed can be measured to within +3% and the radius can be measured to within +2%. Use the differential to approximate the maximum percent error in a. (Hint: The percent error in a quantity is the error in the quantity (da) divided by the quantity (a).) (Ans: 8%)

A three-blade wind turbine, which spins perpendicularly to the ground, is set on a pole that is 38 m tall and completes 5 revolutions in one minute. The length of one blade is approximately 4 m long. One particular blade lies parallel to the ground before the turbine started to spin. a) What is the equation that models the height of tip of this blade as a function of time (in seconds)?

Consider an annular disk rolling down an inclined plane. The annular disk has mass 154 [g], inner radius 8.00 [cm] and outer radius 12.0 [cm]. The inclined plane has a slope that forms an angle of 44.6° with the ground. A.  Suppose that the coefficient of static friction ?s is large enough so that the annular disk rolls without slipping. What is the magnitude of the translation acceleration felt by the annular disk's center of mass in the direction parallel to the slope? B. What is the minimum value that the coefficient of static friction ?s must take so that the annular disk rolls without slipping?

Answer a and  c

The rod O A rotates clockwise with a constant angular velocity of 6 rad/s. Two pin- connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limacon described by the equation r = 200(2 - cos ) mm. (Figure 1) Figure B 600 mm 6 rad/s 400 mm 200 mm 1 of 1 Part A Determine the speed of the slider blocks at the instant 0 = 145°. Express your answer to three significant figures and include the appropriate units. V = Value Submit μA Provide Feedback Request Answer Units ? Next >

George swings a ball around him, in uniform circular motion.  The circle's radius is r.  George inadvertently releases the string, and the ball goes outward.  He catches the string again, and now the ball goes around him at a new rotation rate, with a new radius r + Δr.  Calculate the new rotation rate (in rev/s). r = 3.0 m Δr = 1.0 m Original rotation rate = ωi = 1.1 rev/s The ball's mass is m = 160 grams

A hemispherical bowl having a radius of 6.2m is full of water. If the hemispherical bowl is made to rotate uniformly about the vertical axis at the rate of 30 rpm.   a) Determine the volume of water that is spilled out. Answer in m3   b) Determine the remaining volume of water in the hemispherical bowl. Answer in m3

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